[tex]\huge\mathfrak{\underline{Answer:}}[/tex]
[tex]\huge\bf{=14}[/tex]
[tex]\large\bf{\underline{Given :}}[/tex]
[tex]\large\bf ⟹ x + \frac{1}{x} = 4[/tex]
[tex]\large\bf{\underline{To\: find:}}[/tex]
[tex]\large\bf ⟹ {x}^{2} + \frac{1}{ {x}^{2} } [/tex]
[tex]\large\bf{\underline{Using\: identity:}}[/tex]
[tex]\boxed{\large\bf\pink{(a+b)^2 = a^2 + b^2 + 2ab}}[/tex]
[tex]\large\bf{⟹(x+\frac{1}{2})^2 = x^2 +(\frac{1}{2}^2) + 2.x.\frac{1}{x} }[/tex]
[tex]\large\bf{⟹(4)^2 = x^2 + \frac{1}{x^2} +2}[/tex]
[tex]\large\bf{⟹16= x^2 + \frac{1}{x^2} +2}[/tex]
[tex]\large\bf{⟹16 - 2= x^2 + \frac{1}{x^2}}[/tex]
[tex]\large\bf{⟹x^2 +\frac{1}{x^2} = 14}[/tex]
